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Related Experiment Videos

Multidimensional orthogonal filter bank characterization and design using the Cayley transform.

Jianping Zhou1, Minh N Do, Jelena Kovacević

  • 1Department of Electrical and Computer Engineering, The Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. jzhou2@uiuc.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|June 24, 2005
PubMed
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This study introduces a novel method for designing multidimensional orthogonal filter banks (IIR and FIR) using the Cayley transform. This approach simplifies complex nonlinear equations into linear constraints for efficient filter bank design.

Area of Science:

  • Signal Processing
  • Multidimensional Systems
  • Filter Bank Design

Background:

  • Orthogonal filter banks are crucial in signal processing.
  • Designing multidimensional (MD) orthogonal filter banks is challenging due to the absence of MD spectral factorization.
  • Existing 1D methods do not directly extend to higher dimensions.

Purpose of the Study:

  • To develop a general method for designing orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension.
  • To overcome limitations of traditional 1D design methods for MD applications.

Main Methods:

  • Utilizing the Cayley transform (CT) to map paraunitary matrices to para-skew-Hermitian matrices.
  • Reformulating the design problem from nonlinear equations to linear constraints in the polyphase domain.

Related Experiment Videos

  • Applying the CT to characterize and design MD orthogonal filter banks.

    • Main Results:

    • The Cayley transform provides a one-to-one mapping, simplifying the design process.
    • Para-skew-Hermitian matrices offer linear constraints, making solutions more accessible.
    • Efficient design methods for MD orthogonal IIR and FIR filter banks are proposed.

    Conclusions:

    • The proposed Cayley transform-based method offers an efficient and generalizable approach to MD orthogonal filter bank design.
    • This work provides new design results for both IIR and FIR filter banks in multiple dimensions.